Pick a number, not just any number

Even the pros gravitate to a predictable pattern of numbers, professors find

by Caroline Kettlewell

Chris Gash

Call it another blow to our faith in rational decision-making. In a new paper, UVA professors Patrick Dennis and Benjamin Converse present strong evidence to argue that all numbers are not equal in our minds. Instead, when choosing from an infinite range of possible numbers, even professional stock traders show a clear preference for what the researchers call “prominent numbers”—a specific and repeating subset of round numbers. The researchers theorize that these prominent numbers—1, 2, 5, 10, 20, 50, 100, 200, 500, 1000 and so on—provide an easy mental “zooming” tool, a cognitive shortcut for narrowing the choice of numbers when making numerical judgments in the absence of specific criteria. In other words, when life asks us to pick a number, any number, these prominent numbers function for users of base-10/decimal numbering systems “like landmarks on a map,” says Converse, helping us to quickly and easily refine our selection.

Professors Converse and Dennis studied billions of stock trades and found that they cluster around certain numbers.

Dennis, an associate professor in the McIntire School of Commerce, works in the field of “market microstructure”—the detailed study of stock trades and prices. In a previous study, he noticed a disproportionately frequent pattern of trades in this subset of numbers, even compared with other round numbers.

“It was wildly significant,” says Dennis, explaining that, according to the “rational economic man theory,” a stock purchaser should decide how much was going to be spent on a particular stock, then divide that amount by the share price to determine how many shares would be bought. The pattern of trades Dennis was observing, however, startlingly contradicted that theory.

Intrigued, Dennis collaborated with Converse to investigate further. Converse is an associate professor with appointments in both the psychology department in the College of Arts and Sciences and in the Batten School of Leadership and Public Policy.

In the first study in their paper, which will be published in an upcoming edition of the journal Organizational Behavior and Human Decision Processes, Dennis and Converse studied more than 3 billion stock trades. Stocks, Dennis notes, are bought and sold in quantities that range from zero to very large numbers. Yet despite such a potentially wide range of possible numbers, those more than 3 billion trades nevertheless clearly clustered on the prominent round numbers—500 or 1000, for example—significantly more than even on adjacent nonprominent round numbers such as 400 or 600.

Ben Converse
Jane Haley

Patrick Dennis

In a second study, the authors examined a subset of trades conducted under time-pressured conditions—in the hour following the monthly midafternoon release of the Federal Reserve Open Market Committee statement, which “temporarily forces traders to move quickly” in the hours before the markets close for the day. They compared these trades with a sample of trades from 24 hours later. The result? “It pops out very strongly that when people are rushed, they choose prominent numbers,” Dennis says.

Finally, the two sought further confirmation of their findings through a series of studies conducted via Amazon’s Mechanical Turk service, which pays a small sum to individuals to perform “human intelligence tasks” (such as identifying objects in a photo), and which is proving an increasingly popular tool for conducting research.

These studies demonstrated similar clustering on prominent numbers, which decreased “when judges are able or willing to invest more cognitive effort,” the authors write, providing further evidence that prominent numbers offer a quick cognitive shortcut in numbers judgments.

Converse and Dennis agree that neither could have completed this research without the other’s expertise. They agree, too, that the cross-disciplinary nature of this research, starting with the hard data from stock trades and buttressing that with the additional experiments, gives them particular confidence in the prominent-numbers effect.

They also note observing the pattern in other areas as well, such as currency denominations (the quarter, they acknowledge, is an anomaly) or the zooming scale that you might never have noticed on Google Maps.

But why are these particular numbers, boldfaced in our brains and represented more strongly than other round numbers? One theory Dennis and Converse suggest is evolutionary: Most of us have two hands, with five fingers each, adding up to 10, and thus the pattern of 2, 5, 10 and so forth. “It is 100-percent speculative,” Converse says.

More practically, how might we apply the prominent numbers theory to real-world situations? One use might be as a new tool for forensic analysis, says Dennis, with a pattern of prominent numbers perhaps suggesting fudged data.

Another possibility is one you could experiment with when buying or selling a used car. As Dennis outlines, if you are a buyer, and the selling price is set at a prominent number, it’s possible the seller hasn’t put a lot of careful thought into the pricing, and “it may give you more leeway to negotiate a harder price,” he says. On the other hand, if you’re a seller, offering your item for a more exact, nonprominent-number price could serve as a subtle advantage, a signaling of confidence in pricing that would discourage negotiating.

Dennis and Converse acknowledge that these possibilities are at this point theoretical; their paper simply serves to establish a strong argument on behalf of the existence of prominent numbers. “This paper is a kind of fundamental result,” Dennis says. “Hopefully more people will pile on and see applications in marketing or forensic science.”